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\noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
Banach J. Math. Anal. 2 (2008), no. 2, 85--93\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\footnotesize
\textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach
\textbf{\large{J}}ournal of \textbf{\large{M}}athematical
\textbf{\large{A}}nalysis}}\\
ISSN: 1735-8787 (electronic)\\
\textcolor[rgb]{0.00,0.00,0.84}{\textbf{http://www.math-analysis.org }}\\
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\title[Three--parameter weighted Hardy type inequalities]{Three--parameter weighted Hardy type inequalities}

\author[R. Oinarov, A. Kalybay]{R. Oinarov$^1$$^{*}$ and A. Kalybay$^2$}

\address{$^{1}$ Eurasian National University, Munaytpasov st. 5, Astana 010008, Kazakhstan.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{o$\_$ryskul@mail.ru}}

\address{$^{2}$ Kazakhstan Institute of Management, Economics and Strategic Research, Abay ave. 4, Almaty
050010, Kazakhstan.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{aigerim$\_$k@academset.kz}}

\dedicatory{This paper is dedicated to Professor Josip E. Pe\v{c}ari\'{c}\\
\vspace{.5cm} {\rm Submitted by S.-M. Jung}}

\subjclass[2000]{Primary 26D10, 26D15; Secondary 46E15, 46E30.}

\keywords{Inequalities, Hardy type inequalities, weight functions.}

\date{Received: 14 April 2008; Accepted: 18 June 2008.
\newline \indent $^{*}$ This research work was supported by the INTAS grant Ref.
Nr 05-1000008-8157.}

\begin{abstract}
For $0<r<\infty$ and $1\leq p\leq q<\infty$ we find necessary and
sufficient conditions for the validity of the following inequality:
\begin{eqnarray*}\left(\int\limits_a^bu(x)\left(\int\limits_a^x|g(x)-g(t)|^rw(t)dt
\right)^{\frac{q}{r}}dx\right)^{\frac{1}{q}}\leq C\left(
\int\limits_a^bv(x)|g'(x)|^pdx\right)^{\frac{1}{p}},\end{eqnarray*}
where $u(\cdot)$, $v(\cdot)$, and $w(\cdot)$ are weight functions.
\end{abstract} \maketitle
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